src/ZF/EquivClass.thy
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
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1477:4c51ab632cda 1478:2b8c2a7547ab
     1 (*  Title: 	ZF/EquivClass.thy
     1 (*  Title:      ZF/EquivClass.thy
     2     ID:         $Id$
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1994  University of Cambridge
     4     Copyright   1994  University of Cambridge
     5 
     5 
     6 Equivalence relations in Zermelo-Fraenkel Set Theory 
     6 Equivalence relations in Zermelo-Fraenkel Set Theory 
     7 *)
     7 *)
     8 
     8 
     9 EquivClass = Rel + Perm + 
     9 EquivClass = Rel + Perm + 
    10 consts
    10 consts
    11     "'/"        ::      [i,i]=>i  (infixl 90)  (*set of equiv classes*)
    11     "'/"        ::      [i,i]=>i  (infixl 90)  (*set of equiv classes*)
    12     congruent	::	[i,i=>i]=>o
    12     congruent   ::      [i,i=>i]=>o
    13     congruent2  ::      [i,[i,i]=>i]=>o
    13     congruent2  ::      [i,[i,i]=>i]=>o
    14 
    14 
    15 defs
    15 defs
    16     quotient_def  "A/r == {r``{x} . x:A}"
    16     quotient_def  "A/r == {r``{x} . x:A}"
    17     congruent_def "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"
    17     congruent_def "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"